Underdetermined blind source separation based on relaxed sparsity condition of sources

Recently, Aissa-El-Bey et al. have proposed two subspacebased methods for underdetermined blind source separation (UBSS) in time-frequency (TF) domain. These methods allow multiple active sources at TF points so long as the number of active sources at any TF point is strictly less than the number of sensors, and the column vectors of the mixing matrix are pairwise linearly independent. In this correspondence, we first show that the subspace-based methods must also satisfy the condition that any M × M submatrix of the mixing matrix is of full rank. Then we present a new UBSS approach which only requires that the number of active sources at any TF point does not exceed that of sensors. An algorithm is proposed to perform the UBSS.

Time-frequency approach to underdetermined blind source separation

This paper presents a new time-frequency (TF) underdetermined blind source separation approach based on Wigner-Ville distribution (WVD) and Khatri-Rao product to separate N non-stationary sources from M(M <; N) mixtures. First, an improved method is proposed for estimating the mixing matrix, where the negative value of the auto WVD of the sources is fully considered. Then after extracting all the auto-term TF points, the auto WVD value of the sources at every auto-term TF point can be found out exactly with the proposed approach no matter how many active sources there are as long as N ≤ 2M-1. Further discussion about the extraction of auto-term TF points is made and finally the numerical simulation results are presented to show the superiority of the proposed algorithm by comparing it with the existing ones.

Underdetermined blind source separation by parallel factor analysis in time-frequency domain

This paper presents a new time-frequency approach to the underdetermined blind source separation using the parallel factor decomposition of third-order tensors. Without any constraint on the number of active sources at an auto-term time-frequency point, this approach can directly separate the sources as long as the uniqueness condition of parallel factor decomposition is satisfied. Compared with the existing two-stage methods where the mixing matrix should be estimated at first and then used to recover the sources, our approach yields better source separation performance in the presence of noise. Moreover, the mixing matrix can be estimated at the same time of the source separation process. Numerical simulations are presented to show the superior performance of the proposed approach to some of the existing two-stage blind source separation methods that use the time-frequency representation as well.

Image encryption based on compressed sensing and blind source separation

A novel image encryption scheme based on compressed sensing and blind source separation is proposed in this work, where there is no statistical requirement to plaintexts. In the proposed method, for encryption, the plaintexts and keys are mixed with each other using a underdetermined matrix first, and then compressed under a project matrix. As a result, it forms a difficult underdetermined blind source separation (UBSS) problem without statistical features of sources. Regarding the decryption, given the keys, a new model will be constructed, which is solvable under compressed sensing (CS) frame. Due to the usage of CS technology, the plaintexts are compressed into the data with smaller size when they are encrypted. Meanwhile, they can be decrypted from parts of the received data packets and thus allows to lose some packets. This is beneficial for the proposed encryption method to suit practical communication systems. Simulations are given to illustrate the availability and the superiority of our method.

An extension of slow feature analysis for nonlinear blind source separation

We present and test an extension of slow feature analysis as a novel approach to nonlinear blind source separation. The algorithm relies on temporal correlations and iteratively reconstructs a set of statistically independent sources from arbitrary nonlinear instantaneous mixtures. Simulations show that it is able to invert a complicated nonlinear mixture of two audio signals with a high reliability. The algorithm is based on a mathematical analysis of slow feature analysis for the case of input data that are generated from statistically independent sources. © 2014 Henning Sprekeler, Tiziano Zito and Laurenz Wiskott.

MISEP method for postnonlinear blind source separation

In this letter, a standard postnonlinear blind source separation algorithm is proposed, based on the MISEP method, which is widely used in linear and nonlinear independent component analysis. To best suit a wide class of postnonlinear mixtures, we adapt the MISEP method to incorporate a priori information of the mixtures. In particular, a group of three-layered perceptrons and a linear network are used as the unmixing system to separate sources in the postnonlinear mixtures, and another group of three-layered perceptron is used as the auxiliary network. The learning algorithm for the unmixing system is then obtained by maximizing the output entropy of the auxiliary network. The proposed method is applied to postnonlinear blind source separation of both simulation signals and real speech signals, and the experimental results demonstrate its effectiveness and efficiency in comparison with existing methods.

On the performance of a blind source separation based I/Q-corrector

I and Q Channel phase and gain mismatches are of great concern in communications receiver design. In this paper we carry out a detailed performance analysis of the Blind-Source Seperation (BSS) based imbalance compensation structure. The results indicate that the BSS structure can offer adequate performance for most communication systems. Since the compensation is carried out before any modulation specific processing, the proposed compensation method works with all standard modulation formats.

On the structure and performance of a novel blind source separation based carrier phase synchronization error compensator

In this paper we carry out a detailed performance analysis of a novel blind-source-seperation (BSS) based DSP algorithm that tackles the carrier phase synchronization error problem. The results indicate that the mismatch can be effectively compensated during the normal operation as well as in the rapidly changing environments. Since the compensation is carried out before any modulation specific processing, the proposed method works with all standard modulation formats and lends itself to efficient real-time custom integrated hardware or software implementations.

Blind source separation based on phase and frequency redundancy of cyclostationary signals

This paper presents a new method for blind source separation by exploiting phase and frequency redundancy of cyclostationary signals in a complementary way. It requires a weaker separation condition than those methods which only exploit the phase diversity or the frequency diversity of the source signals. The separation criterion is to diagonalize a polynomial matrix whose coefficient matrices consist of the correlation and cyclic correlation matrices, at time delay .TAU. = 0, of multiple measurements. An algorithm is proposed to perform the blind source separation. Computer simulation results illustrate the performance of the new algorithm in comparison with the existing ones.

Adaptive blind source separation using constant modulus criterion and signal mutual information

We address the problem of adaptive blind source separation (BSS) from instantaneous multi-input multi-output (MIMO) channels. It is known that the constant modulus (CM) criterion can be used to extract unknown source signals. However, the existing CM based algorithms normally extract the source signals in a serial manner. Consequently, the accuracy in extracting each source signal, except for the first one, depends on the accuracy of previous source extraction. This estimation error propagation (accumulation) causes severe performance degradation. In this paper, we propose a new adaptive separation algorithm that can separate all source signals simultaneously by directly updating the separation matrix. The superior performance of the new algorithm is demonstrated by simulation examples